Trig Substitution Without a Radical

by Kelsey
(Atascadero, CA, USA)

State specifically what substitution needs to be made for x if this integral is to be evaluated using a trigonometric substitution:

I think I need to complete the square in the denominator. I have an answer key, however, I am stuck on how to solve it.

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Answer by Pablo:

You are right. Here you need to complete the square. Completing the square you'll get:



After that you're ready to make the trigonometric substitution. I think the most obvious choice is:



This will allow you to simplify the expression a little bit. The messy part is when you need to substitute back, though. But I leave that to you, :).

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